\section{note of 2009.10.05}
It is actually not clear how to do it in many-body theory for two-channel. No one knows.  I have a trail wave-function and that is my assumption.  I can just work on it.  If I can make it self-consistently, it is probably good enough.  

In another sense, what I really want to know is what happens when many-body sets-in, how interaction changes.  No one know exactly what happens.  Maybe I can just use the simple ansantz and that is probably good enough if self-consistent.  
